-4x(2x-8)-8=-12-2x

Solution for -4x(2x-8)-8=-12-2x equation:

-4x(2x-8)-8=-12-2x

We move all terms to the left:

-4x(2x-8)-8-(-12-2x)=0

We add all the numbers together, and all the variables

-4x(2x-8)-(-2x-12)-8=0

We multiply parentheses

-8x^2+32x-(-2x-12)-8=0

We get rid of parentheses

-8x^2+32x+2x+12-8=0

We add all the numbers together, and all the variables

-8x^2+34x+4=0

a = -8; b = 34; c = +4;
Δ = b2-4ac
Δ = 342-4·(-8)·4
Δ = 1284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{321}}{2*-8}=\frac{-34-2\sqrt{321}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{321}}{2*-8}=\frac{-34+2\sqrt{321}}{-16}
$